Question

If E is the mid point of median AD in triangle ABC, then prove that :
Area ($\Delta ABE$) = $\frac{1}{4}$ Area ($\Delta ABC$).

Answer 1

Given, AD is the median of triangle ABC.

So, AD will divide triangle ABC into two triangles of equal area.

Thus,

Area of triangle (ABD) = Area of triangle (ADC)

or, $Area\left(△ABD\right)=\frac{1}{2}Area\left(△ABC\right)$ ... (1)

Again, E is the mid-point of AD. So, BE will be the median of triangle ABD.

So, Area of triangle (ABE) = Area of triangle (BED)

or, $Area\left(△ABE\right)=\frac{1}{2}Area\left(△ABD\right)$

Therefore, $Area\left(△ABE\right)=\frac{1}{4}Area\left(△ABC\right)$ [using (1)]

Hence proved!!